Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in PYTHON3):

Solution:
#######################################################################################################################
#   Author:     BlackFyre
#   Language:   PyPy 3.7
#######################################################################################################################
 
from sys import stdin, stdout, setrecursionlimit
from math import floor, gcd, fabs, factorial, fmod, sqrt, inf, log, log2
from random import seed, randint
from datetime import datetime
from collections import defaultdict as dd, deque
from heapq import merge, heapify, heappop, heappush, nsmallest
from bisect import bisect_left as bl, bisect_right as br, bisect
from collections import defaultdict as dd
mod = pow(10, 9) + 7
mod2 = 998244353
# setrecursionlimit(3000)
 
def inp(): return stdin.readline().strip()
def iinp(): return int(inp())
def out(var, end="\n"): stdout.write(str(var) + "\n")
def outa(*var, end="\n"): stdout.write(' '.join(map(str, var)) + end)
def lmp(): return list(mp())
def mp(): return map(int, inp().split())
def smp(): return map(str, inp().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(m, val) for j in range(n)]
def remadd(x, y): return 1 if x % y else 0
def ceil(a, b): return (a + b - 1) // b
def def_value(): return 0
def def_inf(): return inf
def atoi(s): return ord(s)-ord('a')
def inc(s, n=1): return chr((ord(s)-ord('a')+n)%26+ord('a'))

class XY:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        
def rotate(a,b,c):
    ang = (b.y-a.y)*(c.x-b.x) - (b.x-a.x)*(c.y-b.y)
    if ang == 0: return 0   #0coll, +-clock, --aclock
    else: return ang/abs(ang)
   
n = iinp()
b = lmp()
a = b.copy()
 
s = sum(a)
if s%2!=0:
    print(0)
else:
    s//=2
    dp = l1d(s+1, False)
    dp[0] = True
    for i in range(n):
        for j in range(s, -1, -1):
            if j-a[i]>=0:
                dp[j] = dp[j-a[i]] or dp[j]
                
    if not dp[s]: print(0)
    else:
        flg = False
        for i in range(n):
            if a[i]%2==1:
                print(1)
                print(i+1)
                flg = True
                break
        if not flg:
            print(1)
            gd = 0
            for i in range(n):
                gd = gcd(a[i],gd)
            for i in range(n):
                if (a[i]/gd)%2==1:
                    print(i+1)
                    break